World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
39
Citations
8920
World Ranking
2147
National Ranking
909

Research.com Recognitions

  • 1999 - Fellow of American Physical Society (APS) Citation For his sustained service to the physics community and his original contributions on the applications of mathematics to the study of physical systems

Overview

Ronald E. Mickens is affiliated with Clark Atlanta University in the United States. Their research primarily lies within the fields of mathematics and engineering, focusing on areas such as modeling and simulation, mechanics of materials, statistical and nonlinear physics, mathematical physics, and numerical analysis.

The scientist explores several main topics in their work, including:

  • Fractional Differential Equations Solutions
  • Thermoelastic and Magnetoelastic Phenomena
  • Model Reduction and Neural Networks
  • Numerical methods in inverse problems
  • Numerical methods for differential equations
  • Nonlinear Waves and Solitons
  • Stability and Controllability of Differential Equations

Ronald E. Mickens has contributed to a range of publications, with frequent appearances in venues such as:

  • arXiv (Cornell University)
  • The Journal of Difference Equations and Applications
  • Applied Mathematics Letters
  • Physics Today
  • Applied Numerical Mathematics

Recent notable papers include:

  • Traveling wave solutions of Burgers' equation with time delay (2020, Applied Mathematics Letters)
  • A note on a positivity preserving nonstandard finite difference scheme for a modified parabolic reaction-advection-diffusion PDE (2020, The Journal of Difference Equations and Applications)
  • Approximate rational solutions to the Thomas-Fermi equation based on dynamic consistency (2020, Applied Mathematics Letters)
  • Construction and analysis of a discrete heat equation using dynamic consistency: The meso-scale limit (2023, Applied Numerical Mathematics)
  • A note on a positivity preserving hyperbolic NSFD scheme for heat transfer (2022, The Journal of Difference Equations and Applications)

Frequent collaborators in their research are:

  • Isom H. Herron
  • Talitha Washington
  • Clement McCalla
  • Cui-Cui Ji
  • Weizhong Dai

Ronald E. Mickens has also contributed to book publications, including a work published by World Scientific:

  • Nonstandard Finite Difference Schemes (2020)

The scientist received the distinction of Fellow of the American Physical Society (APS) in 1999 for sustained service to the physics community and original contributions on the applications of mathematics to the study of physical systems.

Best Publications

  • Nonstandard Finite Difference Models of Differential Equations

    Ronald E Mickens

  • Oscillations in planar dynamic systems

    Ronald E Mickens

  • Applications of nonstandard finite difference schemes

    Ronald E Mickens

  • Nonstandard Finite Difference Schemes for Differential Equations

    Ronald E. Mickens

  • Dynamic consistency: a fundamental principle for constructing nonstandard finite difference schemes for differential equations

    Ronald E. Mickens

  • Comments on the method of harmonic balance

    Ronald Mickens

  • Advances in the Applications of Nonstandard Finite Difference Schemes

    Ronald E. Mickens

  • A generalization of the method of harmonic balance

    R. E. Mickens

  • Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition

    Ronald E. Mickens

  • Difference Equations: Theory and Applications

    Ronald E. Mickens

  • An introduction to nonlinear oscillations

    Ronald E. Mickens

  • Exact Solutions to a Finite-difference Model of a Nonlinear Reaction-advection Equation: Implications for Numerical Analysis

    Ronald E. Mickens

  • Discretizations of nonlinear differential equations using explicit nonstandard methods

    Ronald E. Mickens

  • A nonstandard finite-difference scheme for the Lotka--Volterra system

    Ronald E. Mickens

  • Mathematical and numerical study of the duffing-harmonic oscillator

    R.E. Mickens

  • Numerical integration of population models satisfying conservation laws: NSFD methods.

    Ronald E Mickens

  • Nonstandard finite difference schemes for reaction‐diffusion equations

    Ronald E. Mickens

  • Iteration procedure for determining approximate solutions to non-linear oscillator equations

    R. E. Mickens

  • A positivity‐preserving nonstandard finite difference scheme for the damped wave equation

    Ronald E. Mickens;P. M. Jordan

  • A mathematical model for skin burn injury induced by radiation heating

    Weizhong Dai;Haojie Wang;Pedro M. Jordan;Ronald E. Mickens

  • A generalized iteration procedure for calculating approximations to periodic solutions of “truly nonlinear oscillators”

    Ronald E. Mickens

Frequent Co-Authors

Abba B. Gumel
Abba B. Gumel University of Maryland, College Park
Edwin Michael
Edwin Michael University of Notre Dame
George K. Christophides
George K. Christophides Imperial College London
Christophe Letellier
Christophe Letellier University of Rouen
Suzanne Lenhart
Suzanne Lenhart University of Tennessee at Knoxville

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